Families of elliptic curves over cubic number fields with prescribed torsion subgroups
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- by Daeyeol Jeon, Chang Heon Kim and Yoonjin Lee PDF
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Abstract:
In this paper we construct infinite families of elliptic curves with given torsion group structures over cubic number fields. This result provides explicit examples of the theoretical result recently developed by the first two authors and A. Schweizer; they determined all the group structures which occur infinitely often as the torsion of elliptic curves over cubic number fields. In fact, this paper presents an efficient way of constructing such families of elliptic curves with prescribed torsion group structures over cubic number fields.References
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Additional Information
- Daeyeol Jeon
- Affiliation: Department of Mathematics Education, Kongju National University, Kongju, Chungnam, South Korea
- MR Author ID: 658790
- Email: dyjeon@kongju.ac.kr
- Chang Heon Kim
- Affiliation: Department of Mathematics, Hanyang University, Seoul, South Korea
- Email: chhkim@hanyang.ac.kr
- Yoonjin Lee
- Affiliation: Department of Mathematics, Ewha Womans University, Seoul, South Korea
- MR Author ID: 689346
- ORCID: 0000-0001-9510-3691
- Email: yoonjinl@ewha.ac.kr
- Received by editor(s): May 22, 2009
- Received by editor(s) in revised form: October 3, 2009
- Published electronically: May 12, 2010
- Additional Notes: The first named author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 20090060674)
The second named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20090063182)
The third named author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 20090093827) - © Copyright 2010 American Mathematical Society
- Journal: Math. Comp. 80 (2011), 579-591
- MSC (2010): Primary 11G05; Secondary 11G18
- DOI: https://doi.org/10.1090/S0025-5718-10-02369-0
- MathSciNet review: 2728995